enh: provide a demo implementation of refresh provider

[phoenix-ru]

🔗 Linked issue

❓ Type of change

• 📖 Documentation (updates to the documentation, readme or JSdoc annotations)
• 🐞 Bug fix (a non-breaking change that fixes an issue)
• 👌 Enhancement (improving an existing functionality like performance)
• ✨ New feature (a non-breaking change that adds functionality)
• 🧹 Chore (updates to the build process or auxiliary tools and libraries)
• ⚠️ Breaking change (fix or feature that would cause existing functionality to change)

📚 Description

This provides an implementation of refresh functionality to playground-local.
The benefits are:

• we can start E2E testing refresh logic again (which was dropped after feat(#821): Unify local and refresh providers into one #822);
• the implementation is closer to what developers do rather than being a stub.

📝 Checklist

• I have linked an issue or discussion.
• I have added tests (if possible).
• I have updated the documentation accordingly.

[pkg-pr-new]

Open in Stackblitz

pnpm add https://pkg.pr.new/@sidebase/nuxt-auth@901

commit: dd11f72